This invention relates to control systems for growing crystals by the Czochralski technique
Control schemes used in the Czochralski process are typically a combination of feedforward control and closed loop regulators. For controlling the growth dynamics, the only feedback control has been automatic diameter control. Other objectives are achieved in a feedforward manner, using empirically developed input trajectories. Typical feedforward control inputs include selection of crucible and seed rotation trajectories to alter segregation behavior and use of pull rate and power input trajectories to obtain the desired crystal shape and seeding conditions (necking) to reduce grown-in dislocations.
A single input-single-output (SISO) feedback loop is typically used to implement the diameter control, which is sometimes subject to a constraint such as maintaining a desired pulling rate. The diameter error signal is determined from either a weight signal, imaging of the meniscus area, or direct observation by TV or x-ray imaging. System inputs include pull rate and crucible heater power, although several inputs for the meniscus region have been reported. Local closed loop SISO regulators are also employed to maintain desired rotation rates, heater temperatures, and lift rate of the crystal growing system.
The conventional approach to Czochralski systems control has performed adequately for elemental semiconductors such as silicon (Si). However, the increased electronic materials requirements for Si VLSI and ULSI devices and the difficulties in achieving desirable properties for compound semiconductors such as gallium arsenide (GaAs) and indium phosphide (InP), indicates the necessity of developing an improved control strategy.
The coupled nature of the Czochralski process and the material properties of the semiconductor material determine the crystal quality that is achieved. The important coupled process phenomena which determine the resulting dislocation and segregation characteristics of semiconductors include the thermal fluid characteristics of the melt, the interface region's mass and heat transfer, and the thermal stresses in the crystal. As larger crystals are grown, the significance of the different phenomena vary. The problems are especially significant in the growth of compound semiconductor systems, but are also important in other systems such as oxides and elemental semiconductors.
The diameter control structures typically used differ in terms of the measurements and inputs they use. Typical structures include: feedback to heat input, feedback to pull rate input, and feedback to pull rate input kept within bounds by manipulating the heater power. Satunkin and Rossoleuko developed a closed loop diameter control manipulating both pull rate and input power, CRYSTAL RES. TECHNOL., 21 9 1986, p. 1125. They solved the underspecified problem of using two inputs to maintain one output by formulating it as an optimal control problem. The analysis, however, did not include the batch disturbances. Other heat inputs have been studied. Ekhult and Carlberg, J. CRY. GROWTH, 76 1986, p. 317, used infrared heaters to control the meniscus heat transfer using a diameter feedback control structure. Brice et al., J. CRY. GROWTH, 10 1971 p. 133, used cooling jets to overcome heat transfer limitations for crystals that are transparent at infrared frequencies and also reflectors over the melt surface. Srivastava et al., J. CRY. GROWTH, 76 1986, p. 395, has extended the analysis of using jet by examining the radiative and convective heat transfer around the interface region.
While it is generally recognized that the interface shape affects the crystal quality, only limited work has been reported in terms of an active control of the interface shape design. Srivastava has studied the steady-state relation between cooling jets, diameter, and .delta.H, the difference in height between interface and melt. Derby and Brown, J. CRY. GROWTH, 75 1986 p. 227, have reported a method to calculate the required feedforward inputs to maintain the desired interface diameter, R.sub.i, and interface deflection. A limitation to implementing feedforward schemes is that the modelled interface shape is highly dependent on boundary assumptions and therefore is subject to significant modelling error. A feedback scheme will therefore be required to achieve the desired performance. Since disturbances enter both from the crystal and the melt, the interface shape control scheme must be able to correct for both types of heat flux disturbances.
Several researchers have reported the measurement of the melt and crystal temperature distributions, but do not specify how these measurements should be used in the control structure and law. While it is also recognized that the system is time varying, only limited attention has been given to the control design requirements to compensate for the variation. One solution that has been used is to utilize an empirically based open loop feedforward input for either the power or pull rate.
The shortcomings of the conventional control design approach are that (a) the specification of the closed loop control objectives does not explicitly consider the effects of other important process characteristics on the crystal quality, (b) the conventional control structure design does not address the batch disturbances effects, and (c) only limited consideration has been given to the relation between the choice of output variables, measurements, inputs, and controller performance.